Welcome to my blog! You can see all of my latest posts below. If you’d like to start at the beginning, check out my Posts page. Most of my posts form part of a longer discourse, so they build on each other. If you have any comments, questions, or constructive criticisms, then comment away! Cheers, and thanks for reading. 🙂

Case Intensional Logic

In earlier posts (such as this one) I’ve talked about a particular formulation of quantified modal logic which I think is the best way to combine the rules for reasoning about quantification with the rules for reasoning about possibility and necessity – a subject about which there does not seem to be any strong consensus in the literature, as far as I have seen. Recently I updated my personal notes about this, and I thought I would make the document accessible here.

Here is it: Case Intensional Logic.

An interesting thing about this logic is that, starting with just the basic S5 operators for possibility (truth in some case) and necessity (truth in every case), it has the power within the language itself to define variables that correspond to particular cases, operators that indicate truth in those particular cases, alternative modal operators (e.g., operators which obey the rules for S4 modal logic instead of S5, or any kind of accessibility relation between the cases that you wish to impose), and much more. Because of this I think it could be a very powerful tool for formalizing metaphysical theories, and is worthy of greater attention.

A pilot-wave QFT in a 1D universe (updated)

Once again, it has been quite some time since I’ve posted on this blog. I hope to return to writing about philosophy, metaphysics, and theology at some point down the road. But instead of doing that, over the past year or so I’ve gradually been updating my model of a pilot-wave interpretation of quantum field theory in a one-dimensional universe.

To reiterate, this model has two purposes:

First, it shows that a quantum field theory, even a relativistic one, can be formulated as a pilot-wave theory. A common objection to pilot wave interpretations of quantum mechanics is that they only work for non-relativistic QM, so they shouldn’t be taken seriously. Well, this model is a direct counterexample to that claim. The methods I use here for scalar fields in a 1D universe can be adapted straightforwardly all kinds of fields in our familiar 3D universe.

Second, pilot-wave theories enable clear visualization of what is going on in the quantum world in a way that more common interpretations of QM simply can’t achieve. The theory provides determinate values (rather than indeterminate superpositions of values) for the physical content of the universe at every point in space and time, so we can actually see what is going on at the microscopic level. A 1D scalar field theory, like the ones in this model, is particularly easy to portray: just graph the field like any other function of a single variable, and animate it to show the change over time. My hope is that such visualizations would be valuable for making quantum field theory more accessible and engaging.

Also, I just find playing with this kind of model to be fun. I’m weird that way.

The main document outlines 3 models:

  • A free real scalar field
  • A free complex (or 2-component real) scalar field
  • A theory with an interaction between a real scalar field and a complex scalar field

And it discusses how a field may be quantized to produce either bosonic or fermionic behaviour. I have also written a number of supporting documents (including updated versions of some that I had written previously):

With the equations for these models, it should be possible to actually simulate how these field theories behave, and create visualizations. But I feel that goes somewhat beyond my coding ability (or at the very least, my computing power – quantum mechanics with a lot of degrees of freedom is not cheap). Any programmers out there want to take a stab at this and find out what quantum field theory really looks like? I’m still looking for takers…

A pilot-wave quantum field in a box

In introductory quantum mechanics courses, students will often see the “particle in a box” model, where one examines the wavefunction of a quantum particle constrained to move in a 1-dimensional space between two barriers (the “box”).

Bohmian mechanics provides a clearer description of what is may be going on in such a scenario, because in addition to the wavefunction it has an actual particle with a definite location. This clears up the issues that quantum mechanics has in two ways, by resolving the measurement problem and by giving a determinate description of the physical ontology which makes up the world.

But Bohmian mechanics might not have the right physical ontology. What if the world is made of fields, instead of particles? In that case, the “particle” in a box might actually look like this:

Quantum Field in a Box Animation

The image here displays a charge density field (in the upper plot) and a representation of the probability density associated with the single-quantum wavefunction guiding the field (in the lower plot) as they both evolve over time. Here’s what’s happening:

  • The quantum state starts in a superposition where the probability to find the “particle” is concentrated in two different locations, around x=10 and x=20.
  • The field starts in a random configuration (chosen with probability corresponding to the quantum state); it looks something like the probability density but with random fluctuations.
  • The quantum state only has single-quantum (or single-particle) terms in the superposition; consequently, the total charge in the box comes out to be exactly 1, even though (as it turns out) it can be negative in some places.
  • The quantum state initially evolves according to the Schrodinger equation (with the Hamiltonian determined by the natural kinetic energy of the field), and it guides the continuous evolution of the field configuration.
  • (It happens that the length of time I allowed for this stage of the evolution was just long enough for the quantum state to recohere into the original superposition; that was entirely coincidental.)
  • After a while, I switched on a “measurement” interaction to see if the “particle” was in the left half of the box or the right half of the box. (To make the analysis tractable, I also switched off the natural kinetic energy at this point, so that the Schrodinger equation only involved the measurement Hamiltonian.)
  • The measurement pointer (not shown), itself modeled as a Bohmian-mechanical particle coupled to the charge density of the field, moved to record that the “particle” was found in the left half of the box.
  • Simultaneously, the quantum state collapses so that the probability density is constrained to the left half, and the charge density rearranges to be only found in the left half of the box as well.

This little animation provides a glimpse of how particle-like behaviour can arise from the quantization of a continuous field, and what the microscopic world might actually look like if it is made of fields.

To see the math behind the model, click here. If you’re curious to see the python code I used to create the above animation – which you could use to create others like it! – send me a message through the contact page on my site.

A pilot-wave quantum field theory in a finite universe

Rather than blogging about philosophy and natural theology in my spare moments over the past several months, I’ve been working on a model of a pilot-wave interpretation of quantum field theory in a tiny one-dimensional universe.

The purpose of such a model is twofold. One, it shows that quantum field theory (even relativistic QFT) can in fact be formulated as a pilot-wave theory. A common objection to pilot wave interpretations of quantum mechanics is that they only work for non-relativistic QM, so they shouldn’t be taken seriously. Well, this model is a direct counterexample to that claim. The methods I use here for a 1D universe can be adapted straightforwardly to our familiar 3D universe.

Two, a pilot-wave interpretation allows clear visualization of what is going on in the quantum world in a way that more common interpretations of QM simply cannot allow. The theory provides actual values (rather than mere superpositions of values) for the fields at every point in space and time, so we can actually see what is going on at the microscopic level. A 1D field theory in particular can easily be portrayed on a screen; you just graph the field like any other function of a single variable. My hope is that such visualizations would be valuable for making quantum field theory – a vital aspect of modern physics – more accessible and engaging, both for physicists (present and future) and laypeople alike.

You can read my model by clicking here. (Edit: see below for an updated version of this document.) Actually there are two models, one with scalar fields and another with a vector field and a (fermionic) spinor field. I’ve taken it almost as far as I can with just the concept and the equations. To go further, it needs coding to translate the concept into some actual visualizations, or maybe even an applet that would let the user run simple simulations.

Any coders out there who want to take a stab at this and find out what quantum field theory really looks like?

Update: I’ve also written up documents on how to solve the quantum harmonic oscillator and the quantum rigid rotator, systems that form the basis for quantizing the modes of bosonic and fermionic fields, respectively, in a pilot-wave interpretation. The quantum harmonic oscillator is familiar (at least to a student of physics), but you’ve probably never seen the quantum rigid rotator before. Update update: I’ve removed these documents and replaced them with more recent versions: see QHO and QRR.

Further update: I was somewhat unsatisfied with the second model in my earlier document. So, I’ve written up another document (click here!) updating the first model and replacing the second model:

  • The first model (interacting scalar fields) now has some more in-depth explanation, and includes the algorithm to compute the Hamiltonian matrix.
  • The second model (interacting spinor and vector fields) now takes place in a universe with 2 spatial dimensions, rather than one. This allows me to use a massless vector field interacting with the spinor field, which makes the model a much closer analogy to the quantum electrodynamics of our 3D universe.

With the added spatial dimension, the second model is probably beyond any hope of simulating except via supercomputer, but I think it is conceptually valuable, at least.

Shifting views on some metaphysical issues

It’s been quite a while since my last post, and I’m actually considering whether I need to go back and rewrite some of the earlier sections of my blog, before I continue with my exploration of what I believe and why.

Here is the main reason: my view is shifting towards some form of metaphysical realism about universals, away from the nominalism I formerly adopted. When I orginally wrote my post about abstract objects, my grasp of the realism vs. nominalism debate was far more superficial than I realized (much to the chagrin of my present self). Unaware of the range of views within metaphysical realism, I thought nominalism the only alternative to platonism, and I thought SEP article just linked summarized the issue well and showed (together with the arguments in favour of figuralism) that platonism was unnecessary.

I still think that figuralism as a nominalist theory handles certain kinds of abstract objects well – mathematical objects specifically, and perhaps also propositions and related semantic and syntactic objects. However, when I wrote (paraphrasing) that abstract objects such as properties are just useful ways of thinking and speaking about the “ways that things exist,” I should have realized that I had given away the game. In order for there to be any “ways that things exist” to talk about, there has to be more to the story than nominalism.

Looking into this issue further, I am finding myself convinced by arguments in favor of a “constituent ontology,” wherein the properties that make something be the kind of thing that it is are not abstract objects existing in a realm apart (a Platonic view), but instead are immanent to the world around us, as constituents of the entities in the world (a more Aristotelian view). Turns out the ancients and medievals may have known a thing or two about metaphysics, even without our modern scientific knowledge.

I’ve been using interlibrary loans every so often in the past few months to get my hands on heavyweight philosophy books in order to try to figure this out. One of those titles was William Vallicella’s Paradigm Theory of Existence, which contains one such argument for a constituent ontology. He marshals an impressive and sustained argument for his thesis, which is that the only sensible way to answer the question, “what is existence?” (actually he disambiguates that into two questions, but nevermind that for now) is to say that existence is the unity of an entity’s ontological constituents. And the only way for that unity to be intelligible is for there to be a Unifier, a paradigmatically existent individual that grounds the existence of everything else. In fact, this Paradigm of Existence is none other than God.

My shift towards accepting a constituent ontology puts me in a bit of a bind, actually. Because it brings to the fore an aspect of classical theology that I have mostly neglected, and which raises a couple of serious quandries. If existence is the unity of a thing’s ontological constituents, and an external Unifier is required to do the unifying, then God himself must be metaphysically simple in a radical way, so as to not require his own Unifier. Not only must God not be composed of separable parts (the way us humans are composed of head and torso and limbs), he cannot even be composed of different properties, the way a constituent ontologist might say an electron is composed of it’s properties of mass and charge and spin. Instead, all of God’s properties and actions are identical to his nature, which is identical to God himself.

This doctrine of divine simplicity is difficult to understand and raises the spectre of fatalism, as well as being difficult to square with the Christian doctrine of the Trinity. There are responses to these quandaries, of course – philosophers and theologians have been at these questions for hundreds of years, after all. I’m just not sure if I’m entirely satisfied by those responses, yet, or if there’s some loophole in the arguments by which one could evade the most troubling implications of divine simplicity.

Of course, it may just be that I have to eat some intellectual humble pie, and admit that there are some major things about God and the fundamental nature of reality that I’ll never be able to fully understand. (Who would have thought!?) For now, I’ll keep thinking about these matters.

Why I Am A Christian

In my last post, I summarized why I cannot be an atheist, based on all the arguments for and against the existence of God that I have explored on this blog over the past year. For me, the balance of these considerations leans towards belief in God – strongly enough to commit to what I see as the truth, especially in light of what it means for my life, and for everyone’s lives, if it is true.

I can say some similar things about why I am a Christian specifically, not merely a theist, and why I believe that what Christianity teaches is true.

Why I Became A Christian

My earliest reason for believing in what Christianity teaches is simply that this is what I grew up being taught. My parents believed in Christ, and my church community believed, and because I trusted them, that is what I believed as well.

Depending on one’s stage of life and the belief in question, this is a totally valid reason to believe something – but naturally, by the time you are grown, you are in about as good a position as your parents to know the truth about God for yourself, so relying on their authority is no longer enough. Which is why I now have other reasons for believing in Christ than just my parents’ faith. If I did not, I would not remain a Christian.

That being said, I’ll readily admit that this early belief and spiritual environment predisposed me to continue believing the teachings of Christianity, and that hasn’t changed. As I said at the beginning of this part of my blog, I have tried to look at the reasons for and against belief in God as objectively as possible, keeping my biases and predispositions in mind. But I cannot say for certain whether I would have evaluated these reasons the way that I did, had I not been raised to believe the way that I did.

In the end, though, I don’t think this is all that important. People who have been raised in much the same way as me have looked at the same evidence and rejected Christianity on that basis (though obviously I think they have done so incorrectly) – so at the very least my upbringing probably has not determined me to believe what I do. And people who have grown up very differently than me have looked at the same evidence and converted to Christianity on that basis – so even to those without a Christian background, the evidence has force.

My childhood may have biased me in the direction of Christianity, but even trying to take that into account as best I can, I still think there are good reasons to believe that Christianity is true. From my perspective, then, my parents raised me to believe the truth – and that actually makes me very grateful that I was raised the way I was.

Why I Am Still A Christian

So then, my parents’ faith is why I became a Christian at first, but I can give three reasons why I remain a Christian. Here they are.

The first is the evidence for Jesus’ resurrection, which I wrote about in an earlier series of posts. I’ll summarize here (though of course the details are much more in depth). The origin of Christianity is difficult to explain without the disciple’s belief in the resurrection – and the existence of that belief is backed up by the textual evidence. Their belief is difficult to explain without the resurrection appearances and the empty tomb – and those strange occurrences are again backed up by the textual evidence. I see no good way to explain these things naturalistically – and even factoring in some doubt about whether I have correctly assessed the evidence (as I tried to do in my last post*), I remain convinced that the resurrection is the best explanation, and that it sufficiently outweighs the alternatives for one to be justified in believing it.

(*In fact, thinking again about the evidence for the resurrection, I have to admit I think I was underrepresenting its strength when I wrote my last post a month ago, in my attempt to be fair to the other side. I’ve edited the previous post to try to reflect my assessment of the strength of the evidence more closely.)

So, I find there is sufficient evidence to believe that Jesus of Nazareth was raised from the dead after being crucified. And this points to the truth of Christianity: if Jesus rose from the dead, the best explanation of this event is that God was vindicating Jesus’ claim to be the Son of God. If Jesus rose from the dead, it is no stretch to believe that he empowered his followers to proclaim the true religion, and so we can learn the truth from what they wrote. Christianity coheres with the resurrection of Jesus as no other religion (or irreligion) can.

The second reason is my own religious experience. Namely, I have experienced the presence of God in my life, and those experiences have come in a Christian context and have affirmed key truths of Christianity to me, such as the identity of Jesus as God, the forgiveness of my sins through Jesus, the inspiration of the Christian scriptures by God. (These are affirmed via what you could call “spiritual intuition,” I suppose – a inner sense that these things are true.) And while my own experiences have not been so powerful that I could not doubt them, I also know people who have experienced the presence of Jesus much more closely than I have, and many others who have felt what I have, and their testimony lends me trust in what I have experienced.

All these experiences are, of course, subjective and undoubtably influenced by my upbringing and environment. But they cohere with the evidence for the resurrection, and with my other reasons for believing that God exists, so I still have some reason for believing that they are genuine.

The third reason is along the lines of what C.S. Lewis argues in his Mere Christianity. I have written in this blog about the moral argument for God’s existence. I believe we can learn through natural theology that God is the perfect standard of what is Right and Good; that the Being at the foundation of all reality has written a Moral Law on our hearts. But this has a terrifying corollary.

For we do not follow the Moral Law. We kill, we exploit, we lie, we steal. We have all sinned, all failed to live up to the perfect standard in some way. In fact, we humans have an incredible capacity for evil: those who study genocide have consistently observed that ordinary people perpetuate these horrific acts. All of us actualize that capacity to some degree, doing things we ought not to do.

In violating the standard of Right and Good, in disobeying the Moral Law, we have made ourselves enemies of God. And God, being perfectly good, cannot but hate what is evil, cannot but have wrath against us who impugn his goodness and hurt each other – us creatures whom he loves. We are in trouble, and it even seems like God is in a conundrum. How can his love for us on one hand be reconciled with his hatred for our evil on the other?

Christianity teaches that we have this distressing problem (to put it mildly) – agreeing with natural theology. But it also teaches the solution. In our imperfection and finitude we could never hope to get out of the problem ourselves, and so God himself has provided a way for us to be brought back into right relationship with him. The love and holiness, justice and mercy of God come together in the cross of Christ. And so, it seems to me that Christianity overcomes a potential contradiction in the perfect goodness of God in a way that no other religion does.

Of course, I would need to go into more detail about what exactly Christianity teaches, and how this all works, in order to fully show why I think the above paragraph makes sense. And I intend to do that, in future posts. Suffice to say for now that this Good News – this hope of salvation from our sins, uniquely displaying the perfect goodness of God – is a reason I believe that Christianity is true.

(All of that is to say that I believe Christianity is true; actually being a Christian – living from faith in Jesus and loyalty to him, obeying what he has commanded us – is harder. I’m still working on that part.)


That pretty much wraps up what I wanted to do with this section of the blog – explore the reasons for and against belief in God, and explain why I find belief in God, and Christianity in particular, to be rational. I will be taking a break from this blog for a while before starting the next stage (life has gotten busy lately). When I come back, I will continue exploring my beliefs and my reasons for them – this time, focusing on what Christianity entails.

Why I Can’t Be An Atheist

Almost a year ago I started posting about my exploration of what I see as the strongest arguments for and against the existence of God, and I started writing these posts several months earlier than that. Almost half of the posts on my blog so far have been directed at this question. (And on top of that, apparently my average word count per post has been higher this year than last!) So it has been a fairly long project.

Looking back over all of the thoughts I’ve gathered, here is where I find myself: I cannot be an atheist.

I can imagine why someone might be an atheist. I can imagine how you might weigh the considerations differently so that atheism is reasonable, even. But for me, that is not an option. For me, the arguments for God’s existence substantially outweigh those against.

What I Have to Believe to be an Atheist

Here is what I would have to believe in order to be an atheist:

  • The principle of sufficient reason is false, and the fact that the universe seems to work like it is true is just one huge coincidence. Abductive and inductive reasoning is invalid, and most of our scientific reasoning is undermined.
  • There is ultimately no reason why the universe (or anything at all) exists, or is the way that it is.
  • There is no explanation for the finely-tuned structure of the physical universe, except perhaps for vastly improbable chance.
  • The existence of consciousness is inexplicable, and in fact, because of this, the connection between our experiences and any external reality becomes dubious.
  • There is no such thing as objective morality, no right or wrong. Morals are just subjective impressions foisted upon us by our evolutionary and cultural history, and we have no fundamental obligation to follow them.
  • There is no such thing as objective beauty. Any sense of the transcendent we have in the sight of something beautiful; any experience of awe and wonder at the world around us; is empty and illusory.
  • There is even no such thing as objective rationality, and it is dubious whether our ways of reasoning, even deductively, are capable of reliably producing truth.
  • In a universe void of the transcendentals of truth, goodness, and beauty, with no teleology in our creation, living insignificant lives in the overall scheme of things, and universally destined for non-existence no matter what we do, life is ultimately without value, purpose, or meaning. (And we can pretend otherwise, but it doesn’t change the reality.)

In contrast, in exchange for the meaningfulness, explanatory coherence, and firm foundation that theism brings to one’s worldview, I only have to accept these tensions in order to be a theist:

  • I cannot fully understand why God would create a world containing evil and imperfection (though I can come up with some plausible reasons why he might do so, in general).
  • I cannot fully understand why God would not make more complete revelation of himself universally available, instead revealing himself in particular places and times in history and allowing many false religions and ideas about him to propagate (though again, I can come up with some plausible reasons why he might do so, in general).
  • I cannot fully understand how God has acted in regards to salvation, eternal life, and those who are excluded from that destiny (but logically, I see no barrier to things turning out in a way that accords with his goodness).

I could, perhaps, be accused of playing things up a little bit here for rhetorical effect. I am not saying that these conclusions are obvious and rationally compelling for everyone. I don’t think all atheists are inherently irrational. But at the end of the day, I do think they are mistaken. Under the light of the arguments for God’s existence, I find that atheism results in absurdity.

I admit haven’t spent as much time exploring and responding to the arguments against God’s existence on this blog as I would have liked to – there is much more that could be said (and has been said, elsewhere on the internet) regarding those subjects. And ideally, in a wrap-up post like this I would be including a quantitative assessment of the cumulative strengths of the reasons for and against belief in God, accounting for the degree of dependence or independence between the different arguments.

I will at least attempt to do that quantitative assessment, briefly, here. (“Briefly.” Ha.)

Quantifying Belief

In the comments on a post a few weeks back, one gentleman (who his own blog worthy of reading) suggested a high-level categorization of the arguments for and against God’s existence, and I think it is a good way of looking at things:

  • Argument from Reality: theism is the best way to explain some fundamental features of reality (encompassing the cosmological, teleological, noetic, and axiological arguments).
  • Argument from Imperfection: atheism better explains the fact that reality is full of imperfection (encompassing the problem of non-god objects, the problem of evil, and dysteleological arguments).
  • Argument from Revelation: theism is supported by experiences of God and the evidence of God’s actions in history (encompassing the epistemological and historical arguments).
  • Argument from Indifference: atheism better explains the apparent indifference of religious revelation (encompassing the problem of divine hiddenness, the problems of religious pluralism and religious disagreement, and the problem of exclusivity).

The argument from imperfection is paired against the argument from reality, and the argument from indifference is paired against the argument from revelation. (One further category, which I’m not going to consider in this analysis due to the difficulty of casting them as abductive arguments, would have the ontological argument on the side of theism, and contradictions in the concept of God on the side of atheism.)

Now what I want to do is run a Bayesian analysis of the odds for theism over atheism, considering each of these arguments in turn: reality (R1), imperfection (I1), revelation (R2), and indifference (I2). Using the odds-ratio form of Bayes’ theorem, and iterative use of the fact that P(A & B) = P(A|B)*P(B):

\frac{P(G|R1,I1,R2,I2)}{P(\sim G|R1,I1,R2,I2)}=\frac{P(I2|G,R1,I1,R2)}{P(I2|\sim G,R1,I1,R2)} \times \frac{P(R2|G,R1,I1)}{P(R2|\sim G,R1,I1)} \times \frac{P(I1|G,R1)}{P(I1|\sim G,R1)} \times \frac{P(R1|G)}{P(R1|\sim G)} \times \frac{P(G)}{P(\sim G)}

To make estimating these probabilities a more reasonable task, I am considering them all to be conditional on some level of background knowledge which frees us from having to consider the probabilities of many irrelevant specific contingent data about the world. In this way the focus can be on whether each worldview in consideration (theism or atheism) has the resources to explain the high-level facts we are interested in.

Even with that, it is hard to pin down some of these numbers, so I will actually model them as a distribution of probabilities. More on that below.


First, I think it is fair to consider the prior odds of theism (and atheism) to be one to one, or approximately so. I mentioned Paul Draper’s “low priors” argument a few posts ago, but as I said then, I don’t think it is successful. The intrinsically symmetric alternatives that he considers, “source physicalism” and “source idealism,” both need to be further specified to account for the full range of data. And I see no reason to think that theism must be further specified from source idealism than a viable form of atheism must be from source physicalism.

So P(G)/P(~G) = 1.


Now, does the existence of God provide a solid ground for the fundamental features of reality (e.g. existence, appearance of design, consciousness, objective value) that need to be explained? Without considering any of the imperfections in reality – that is the next argument, not this one – I would say the answer is a solid yes. So I will set P(R1|G) = 1.


The argument from reality is atheism’s weak point, in my mind. In order to explain these fundamental features of reality, it faces all the difficulties that I raised above. (And I’m trying to stick to the rational difficulties, but there are serious existential difficulties as well.) My initial impulse is to rate this probability no higher than 0.01, with 0.001 being closer to what I would put it at on most days. Just the failure of the PSR alone, I think, is worth putting it below 0.01.

That is probably a bit extreme, so I will ease off by a factor of 2 and say P(R1|~G) = 0.002 to 0.02. (Median value 0.006.)


Of the considerations that could go under the argument from imperfection, I have only specifically addressed the problem of evil on this blog. But the others, the problem of non-god objects (why would God, a perfect being, create anything at all?) and dysteleological arguments (why would God create things that appear poorly designed?) do not add much weight to it, honestly. And given what I think are good responses to the problem of evil, I don’t think this probability needs to be much lower than 0.5.

But recognizing that the argument from imperfection does cause some tension for theism, I will estimate P(I1|G) = 0.1 to 0.4. (Median value 0.21.)


Assuming atheism could overcome the argument from reality, can it explain all the imperfections and evils that we see? Yes, completely. P(I1|~G) = 1.


The question here is whether it makes sense for God to provide some revelation of himself and whether theism can account for the kind of examples of revelation that we see. I think the answer is yes, in general, and that this probability is pretty close to 1. To make things simpler, any doubt about this can be transferred to a boost to the next probability. So P(R2|G) = 1.


For me, this probability would be pretty close to 1 (making the argument from revelation quite weak) if it were not for the events surrounding Jesus’ death and the origin of Christianity. I do think atheism has difficulty explaining the evidence that we have for what happened there.

Nevertheless, assessing the argument for the resurrection is a complicated matter, and I am fairly uncertain about just how much force it has. My initial thought is to put this probability anywhere from 0.01 to 0.5. To offset the value of 1 given to the corresponding probability on theism, I will set P(R2|~G) = 0.05 to 0.6. (Median value 0.22.)

(*Note: in an earlier version of this post, I instead set P(R2|~G) at 0.15 to 0.75, wanting to be generous to the other side. But upon later reflection, I felt this really underrepresented my assessment of the strength of the evidence, even taking my uncertainty about that into account. With the original numbers, the median value for my overall probability for God’s existence was about 91.5% instead of 95.3%.)


The question that theism has to face now is why God’s revelation of himself is apparently so ineffective and localized. Why would God not make his existence more obvious? Why is there so much religious confusion? How could God leave people in this state of uncertainty, and then condemn them to hell?

The kinds of considerations that I have raised in response to these things in that past few posts go a ways to reducing the tension that the argument from indifference brings to theism – but I find it more difficult to overcome than the argument from imperfection. Let us say that P(I2|G) = 0.05 to 0.3. (Median value 0.13.)


Finally, can atheism explain the apparent indifference of religious revelation? Again, it can do so perfectly. P(I2|~G) = 1.

For each of the four probabilities with a range of values, I have modelled them using a logit-normal distribution with the upper and lower values listed above set to the 10th and 90th percentiles. These are what the distributions look like:


subjective distributions

And once these random values are put into the Bayesian equation, and the result converted into a distribution for the posterior probability that God exists (using 10,000 sets of randomly generated numbers to estimate the distribution), this is what I end up with:

subjective distribution output smoothed

This ranges from 82% at the 10th percentile to 98.8% at the 90th percentile, with a median probability of 95.3%. (An equal probability for theism and atheism, at 50%, is down below the 1st percentile in this distribution.)

So, there you have it. Given how I’ve weighted the above arguments, I should on average be a bit more than 95% confident that God exists.

Faith and Reason

This value (or distribution of values) represents an assessment of the strength of the rational justification for belief in God. Obviously, it is a product of several subjective judgements, and different people could weight the arguments differently and get a different number out as a result. On a different day, I myself might feel that different numbers are more appropriate than the ones I have given here. So this number shouldn’t really be thought of as any kind of precise determination of my level of belief in God.

But even more than that, while rationality is extremely important, at the end of the day I have to admit that it isn’t the only consideration that goes into forming one’s beliefs. There are existential considerations as well: considerations about finding meaning and purpose in our lives, and about how our beliefs are going to impact the way we live. So while I definitely think that there are good reasons to believe in God – 95% isn’t insignificant, after all – there is more than that. And the meaning and purpose of life that I find in the theistic worldview draws me, essentially, to commit to what I see as the truth.

The existence of God is too important, and the implications too far-reaching, for it to be practical to be indefinitely weighting the reasons for and against theism, holding that left tail of the distribution in mind and wondering if it will change. This gets back to something I wrote about at the very beginning of my blog: we need critical thinking, but we also need epistemic faith. When we see good reasons to accept a belief – as I see good reasons to believe in God – we should trust that, and not linger in unnecessary skepticism.

Basically, what I am saying is that I am willing to take that last 5% on faith, and I think it is proper to do so. I will trust what I have good reason to believe.

This does not mean that I think I should seal up the issue of belief in God and never subject it to scrutiny again. If something comes up that makes me think about how I’ve weighed the evidence, or if I come across some new consideration that could affect the balance, I am willing to take a look at it. (Granted, given the scope of my exploration of this issue so far, I admit that I find it unlikely that something will ever impact my belief so much as to make me change my mind. But I want those who disagree with me to be open to changing their mind, so I should probably exhibit the same attitude!)

So, that is why I am not an atheist. In my next post, I will write a little bit more on why I believe that Christianity, specifically, is true.

The Problem of Exclusivity

In my previous post, I argued that the problem of religious pluralism (that the diversity of the world’s religions makes it unlikely for a non-pluralist religion like Christianity to be true) is derivative: the strength of this argument borrows its strength from the problem of divine hiddenness (that the widespread unbelief in God’s existence is improbable, if God really did exist).

Specifically, I concluded that the following ratio, measuring the strength of the problem of religious pluralism, is the same magnitude as the probability that God would choose to remain hidden:

\frac{P(G|E,K)}{P(\sim G|E,K)} \simeq P(H|G,K)

(Where G is the hypothesis that the Christian God exists, E is the fact of religious diversity in the world, H is the hypothesis that God chooses to remain hidden to some degree, and K is our background knowledge.)

This means that the problem of religious pluralism is only as good as the problem of divine hiddenness – and moreover, it isn’t independent of it. And the considerations that I brought up two posts ago, when I wrote about the problem of divine hiddenness, basically amount to reasons to think that P(H|G,K) may not be that low after all. (The relationship between the two problems also means that as long as there is value for God in allowing religious diversity – say, because the existence of contrasting viewpoints ultimately clarifies the truth in the long run – that adds further reason for God to remain partially hidden.)

There is one issue relevant to both of these problems that I haven’t addressed yet. What overriding reasons could God have to remain hidden, and allow religious diversity, if having certain correct beliefs about God is essential for salvation and eternal life?

That is, we can suppose that many of the reasons for God to allow non-belief (which come down to “more and better relationships in the long run”) are ultimately rooted in people eventually being able to receive eternal life and experience the greatest possible good. But if people are excluded from eternal life unless they accept Jesus as their Lord and Saviour in this mortal life – in order to do which, they must believe that he exists – how can any of those reasons override the motivation for God to ensure belief? How can a loving God deny the opportunity for eternal life to so many people?

This is the problem of exclusivity in a nutshell. And to my mind it is the most significant problem underlying both the problem of divine hiddenness and the problem of religious pluralism.

The Fate of the Unevangelized

One of the core claims of Christianity is that eternal life is available through the work of Jesus Christ alone. The problem of exclusivity cuts particularly hard against Christianity if this means that only through conscious faith in Jesus Christ can someone be saved. This is definitely the stance that some Christians take, and arguably, it was at least a kind of “working assumption” for the apostles in the early church:

“For everyone who calls on the name of the Lord will be saved. How then will they call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching?” – the Apostle Paul, Romans 10:13-14

But if you were to ask Paul whether he meant that salvation was so exclusive that it’s only those who have heard someone preach about Jesus who even have a chance, I think he might point to what he wrote just a few verses later in that chapter:

“But I ask, have they not heard? Indeed they have, for ‘Their voice has gone out to all the earth, and their words to the ends of the world.’” – the Apostle Paul, Romans 10:18, quoting Psalm 19:4

(“Their voice” in Psalm 19:4, which Paul quotes here, is referring to the way that God’s glory is revealed in what he has made, available for all to see.)

Here Paul seems to suggest that people can come to have the appropriate kind of faith to be in a right relationship with God, without having the particular knowledge of what Jesus has done. We have examples in the Old Testament of figures like Melchizedek and Job, who are portrayed as righteous, even though they are outside of God’s covenant with his people. And the Bible never affirms the notion that people are judged simply for not having heard of Jesus – rather, God judges us on the basis of what we have done with the knowledge and ability that he has given us. (This, I take it, is part of what Paul is saying in Romans 2:12-16 and Romans 5:13, for example.)

So there is room within Christian belief for at least a moderately inclusivist position: the idea that the salvation which is made possible by Jesus is accessible by having an appropriate kind of faith in God, and that this faith may not require conscious knowledge of what Jesus has done. God gives grace sufficient so that salvation and eternal life are available to all.

However, there is a little more that the problem of exclusivity can say against Christian belief. Evangelism is a central part of Christianity. (I must admit it is far more central than I act as if it is, to my shame.) Presumably this indicates that in some way, hearing the gospel gives a person a better chance of developing the right kind of faith in God by which they can be saved – otherwise the motivation for evangelism would not be as great. How then is it fair that God does not give this opportunity – the opportunity to hear the gospel – to everyone?

The concern here is that there are some people who never hear the gospel and are forever lost, failing to gain eternal life – but who would have been saved if only they had heard the gospel. On the face it seems very probable that if there is anyone who never hears the gospel, then surely some of these people would have been saved had they heard it. And then it seems that the eternal damnation that these people suffer is just a result of the various historical and geographical contingencies which led to the fact that they never heard the gospel.

I say that this concern seems very probable on the face, but the truth is that here we are again faced with epistemic limitations that make it difficult to assess the probability this claim. We cannot see inside people’s hearts and minds – often I think we have trouble discerning what is going on in the depths of our own hearts – and it is even harder to see what would be inside people’s hearts and minds were they to be in a different situation. So we have no direct ability to verify this claim. But then we can only indirectly assess it, by inferences and assumptions.

And an implicit assumption behind an assessment of high probability for this concern is a kind of inductive presumption of uniformity. It is the idea that if in one group of people a certain portion have a certain trait, then in a similar group of people we should expect a similar portion to have that trait. Since there are people who grew up without hearing the gospel who then do accept it upon hearing it, we expect that there should be people in groups who have never heard the gospel who would accept it upon hearing it.

Here now is the flaw in this concern. This kind of reasoning is powerful and very often valid – we use it all the time in everyday life and in science – but it is liable to not properly account for occurrences and circumstances that are intricately tied up with God’s providence over history. If there are reasons for God to choose some degree of hiddenness (such as those I explored a few blog posts ago), there is a way God can “have his cake and eat it too:” God can create a world in which he remains hidden, yet there are still no accidents of history or geography leading to people being lost who would otherwise have been saved.

Let me try to clarify what I mean. First, I am suggesting that people are able to enter into a right relationship with God without having heard of Jesus Christ (even though what Jesus did is ultimately necessary for that relationship to be possible). And second, I am then suggesting that, through his foreknowledge, God has arranged the world in such a way that there simply are no people who are “accidentally” lost – people who are lost, but who would have been saved if only God had put them in circumstances where they had heard the gospel.

On this proposal, someone who is lost without hearing gospel is lost not because they did not hear about Jesus, but because they failed to enter into a right relationship with God – something which was possible for them to do. And moreover, it happens that even if they had heard the gospel, they still would not have entered into a right relationship with God, and so the fact that they are lost cannot be chalked up to historical or geographical accident. And the reason why God would create the world in this way is simply that he is too good to create people without the possibility of salvation, and too good to create anyone whose failure to be saved is so circumstantial.

This suggestion basically follows what William Lane Craig propounds (for example, in this article; for a more nuanced possibility see Kirk MacGregor’s article here; and I think there is room for even more nuance and depth in that analysis, if there are any aspiring theologians or philosophers of religion reading this). If this suggestion is reasonably plausible on the assumption that God exists – and because of God’s goodness and the reasons he may have for remaining hidden, I think it is plausible – then it goes a ways towards removing the overriding reason against the plausibility of God’s remaining hidden.

Another possibility that gets around the concern about the fate of the unevangelized is that there simply are no people who never hear the gospel, because anyone who never had an appropriate chance to respond to God in this mortal life is given a chance in the afterlife. Some Christians believe that this is hinted at in 1 Peter 3:19, for example. (I am somewhat doubtful that this is the intended meaning of that verse, but see here for an article laying out this possibility.) Again, the reason that God would do this is rooted in his goodness, and if this suggestion is plausible, it eases the problem of exclusivity.

The Fate of the Lost

There is one more objection to Christian belief that is relevant for this post. That, of course, is what may be called the problem of hell.

The traditional belief within Christianity is that everyone who fails to receive eternal life – everyone who is excluded from experiencing the ultimate good – instead ends up in hell for eternity, in an unending state of suffering. And the horror of this idea provokes the question, how can this be good? How can a loving God subject any of his creatures to such a destiny?

There are a couple of things that I would say in brief response to that.

The first is that it is quite reasonable to think that not everyone can be saved. In order for heaven to be what it is – an eternity of experiencing the ultimate good of perfect relationship with God and with everyone else – the saved in heaven need to go on making the right choices, to maintain that state of perfection instead of marring it, and they need to go on making those choices forever. Nobody besides God knows perfectly how to make the right choices, so in order to enjoy heaven, one must submit to God’s will. There is no getting round that. And for the relationship with God to be fully good, it must be entered into freely, so God cannot force the kind of submission to him that the enjoyment of heaven requires.

But this means that anyone who will not freely submit to God ultimately cannot join the ranks of heaven, basically out of logical necessity. This makes it extremely plausible that universalism, the idea that everyone will be saved, is false. But then something has to be done with the people who are not saved. (Just what that something is, I will get to in a moment.)

The second thing is that the exercise of punishment, as an act of retributive justice against wrongdoing, arguably flows out of God’s goodness and is in no way contrary to it. It is an aspect of God’s goodness that he punishes evil. And despite what most everyone would say at this point – that they haven’t done anything so evil as to deserve eternal torment as punishment – the fact is that we tend to minimize and ignore the extent of our wrongdoing. We hurt others more than we admit. We do worse than we often recognize in hindsight, after we have edited our accounts with excuses. We transgress against the perfect goodness of God.

So much of the problem of evil is really the problem of our evil. This is not to say that humans are all bad all the time, but it is not a tenet of Christianity that humans are “basically good.” Our God-given potential can be used for both good and evil, and often and unfortunately, we use it for evil. God offers mercy, but if that mercy is spurned, his punishment, his justice, is not wrong. It is a righting of wrongs.

The third point is that the traditional Christian teaching of eternal conscious torment may not, in fact, be correct. There are Christians who hold that the suffering of hell is simply the miserableness of existence apart from God and the joys of heaven. (C.S. Lewis vividly depicts something along these lines in his work The Great Divorce.) And the folks at Rethinking Hell, among other places, make a good case that what the Bible actually teaches is annihilationism (also known as conditionalism or conditional immortality), which says that the ultimate fate of the lost is cessation of existence. If eternal conscious torment is incompatible with God’s goodness, that may just be a strike against that doctrine, not against the existence of God.

I won’t go any further into those in-house debates in this post. But my point is, when it comes to the fate of the lost, we can trust that God will act in a way that accords with his goodness and justice, whichever that way may be. (That trust is on the basis of our reasons for thinking that God is good in the first place; coming from the moral and ontological arguments in natural theology; from religious experiences; and from the teachings of Jesus and scripture via the argument from the resurrection.)


The responses I have given to the problem of exclusivity (and along with it, to the problems of religious pluralism and divine hiddenness) are admittedly speculative. But like my responses to the other atheistic arguments in the last three posts, I think they are sufficient to noticeably diminish the strength of this problem. Given these considerations, I do not think we can claim with confidence that the particularity of Christian belief is an overriding reason against God’s remaining hidden and allowing the religious diversity that we see.

The Problem of Religious Pluralism

Perhaps a disclaimer before I begin this post: the title is referring to the fact that religious diversity or pluralistic perspectives are supposed to present a challenge to religious views which claim certain things are true, to the exclusion of other views. It is not intended to imply anything negative about the value of religious diversity or religious pluralism, and should not be read as such. On that note, let’s explore this topic.

It is an evident fact in today’s world that humanity has held, and continues to hold, a great diversity of religious beliefs. This is often said to pose a problem for those who believe in a particular religious tradition – and it is said to especially pose a problem for religions, like Christianity, which claim that there is only one way to obtain salvation, eternal life, and the greatest possible good that a person can experience.

Whatever problem it is that is supposed to be presented from there mere facts of religious diversity, I am calling the problem of religious pluralism. That will be the topic of this post. I’ll try to show why, from my perspective, the religious diversity in the world is not an overwhelming problem for belief in God, or for Christian beliefs in particular.

The problem that religious diversity is supposed to present specifically to religions that claim to be the only way to salvation, I am calling the problem of exclusivity, and that will be the topic of the next post.

Attitudes Towards Religious Diversity

First, let’s take a look at the different attitudes a person might have towards the diversity of religious beliefs that there are:

An attitude that some people express is that all religions are true. Call this naïve religious pluralism. It is naïve because it is obviously false: the world’s religions make conflicting claims. Some religions say there is one God; others say there are many. Some religions say God and the Universe are One; others say they are distinct. Some religions say there is reincarnation; others do not. They cannot all be true. (This goes even for doctrinal differences within a religion.)

(The naïve religious pluralist might try to avoid this objection by embracing relativism about religious truths: every religion is true for its adherents. But as I have argued before, relativism is not only false but incoherent. There is no rational escape down that path.)

So another attitude that people may hold is that all religions are technically false, but they are all effective in bringing about the ultimate human good. This can be called sophisticated religious pluralism. The idea here is that all the different religions are humanity’s attempts to relate to the Divine or the Ultimate Reality, and to access salvation or enlightenment, and that all of these religions are noble and valuable attempts – even if none of them can ever really be true because of the ineffable nature of the Real, or whatever it is that it out there.

Another attitude, of course, is that all religions are simply false, because there is no supernatural Ultimate Reality to be found. This is naturalistic atheism, and it would explain religious diversity as no more than a collection of delusions that have evolved alongside humanity’s capacity to reason about the world.

And the last attitude one may hold is that some religion is true – this is religious particularism. Usually, the person who holds this attitude believes that their religion is the true one, but that need not be the case: someone can think that there is a particular set of religious belief which are true, but that they do not know what they are (or if anyone has even discovered them yet).

Narrowing In On The Problem

It should be obvious that, if the atheist or the religious pluralist thinks that the religious particularist has a problem with the facts of religious diversity, that problem cannot be simply that the particularist claims a particular religion is true. The (sophisticated) pluralist and the atheist also make particular truth claims about reality – they also say that certain things are true, and that any belief system which denies those claims are false:

  • Atheism says that there is no supernatural reality, and that all the world’s religions claiming otherwise is false.
  • Pluralism says that the supernatural reality is not truly as any of the world’s religions claim, and that all religious paths are valid, contrary to the tenets of all particular religions.

Meaning that pluralism and atheism are not really any less particular than religious particularism.

So just what is the problem with religious particularism? One false start at this problem is sometimes alleged: that particular religious beliefs cannot be true, or cannot be justified, because they are so often culturally relative. But that is not correct. Beliefs may very well be true, and even justified, even if they happen to be correlated with a particular culture. (Pluralism and atheism are fairly correlated with our modern secular culture, yet their proponents surely think their beliefs are true and justified!)

More frequently, it is alleged that adherents of religious particularism are arrogant, narrow-minded, and intolerant for believing that only they have the truth, and that everyone else is wrong and should believe as they do instead. But again, this is not the case.

It is not arrogant to believe something if you have sincere and valid reasons for believing it. It is not narrow-minded to believe one thing instead of another, when one is logically incompatible with the other. It is not intolerant to think that others should come to believe the same thing as you, when you believe that we can experience the greatest good via knowing the truth. (And even if it were arrogant or intolerant, that would not prove that religious particularism was false.)

Perhaps the problem of religious pluralism is intended as an instance of the epistemic problem of disagreement: the diversity of religious beliefs should cause us to doubt, since, on a whole, humanity is filled with people who are roughly our epistemic peers, yet they disagree with us. But if this is the problem, it also cuts against the pluralist and the atheist, not just the particularist. (Not to mention that the epistemic import of disagreement is a subject itself containing a great diversity of beliefs and disagreement, so there is no consensus that this argument is effective!) And this objection does not actually work against the truth of religious particularism, merely the justification for belief in it.

It seems to me that the best way to present the problem of religious pluralism is actually this: atheism or religious pluralism explains the facts of religious diversity better than religious particularism does. In other words, it is claimed that religious particularism is an inferior explanation for religious diversity than the alternative, and therefore the alternative is preferred by abductive reasoning.

Explanations of Religious Diversity

Inference to the best explanation can be roughly formalized using Bayes’ theorem. For example, the claim that atheism better explains the diversity of the world’s religions than Christianity does can be stated by saying that the conditional probability of atheism is greater than the conditional probability of Christianity, given the facts of religious diversity.

Let’s say G is the hypothesis that the Christian God exists. The negation of G, symbolized by ~G would include (at least) all other particular religions, religious pluralism, and naturalistic atheism. Now let’s say E is the evidence of religious diversity, and K is our background knowledge: all the relevant facts we know with G and E (as well as ~G and ~E) cordoned off, so to speak.

Then the objection against belief in this particular religion is:

\frac{P(G|E,K)}{P(\sim G|E,K)}<1

Using Bayes’ theorem this ratio is the product of two other ratios:

\frac{P(G|E,K)}{P(\sim G|E,K)}=\frac{P(G|K)}{P(\sim G|K)} \times \frac{P(E|G,K)}{P(E|\sim G,K)}

In other words, the odds ratio for the existence of God, conditioned on the evidence of religious diversity, is the product of the prior odds ratio and the Bayes’ factor coming from the evidence in consideration.

The prior odds ratio depends pretty strongly on what is included in the background knowledge, K, and how that knowledge is evaluated. From my perspective, it makes sense to include as much in K as we can while keeping the question of G or ~G and E or ~E open. Therefore, it may include the kind of information that goes into the other arguments for or against God’s existence: the arguments from natural theology, the historical argument for the resurrection of Jesus, the problem of divine hiddenness, and the problem of evil.

Given this background knowledge, my assessment is that the prior odds ratio for G is fairly high, with the arguments from natural theology outweighing the force of the problems of evil and divine hiddenness. But, since we are interested here in exploring how the problem of religious pluralism affects the balance of things, I think it is reasonable to ignore the prior odds for now, and focus on the Bayes’ factor.


An aside on the scope of the background knowledge:

Note: the argument for the resurrection is pertinent to G specifically, since G is the hypothesis that the Christian God exists. If the information relevant to the resurrection argument is removed from the background knowledge K, there are two options. One is for that information to be included in E. But that would arguably make the evidence E too specific, lowering the probabilities P(E|G,K) and P(E|~G,K), simply due to the fact that any event becomes highly improbable when you specify it very precisely, and making those probabilities harder to estimate. Not only that, but it would artificially inflate the Bayes’ factor, since P(E|G,K) would not be reduced as much as P(E|~G,K) due to the higher explanatory power of G over ~G for the evidence surrounding the resurrection.

The other option is to not consider that information anywhere. Then the prior odds for G are reduced, but this does not tell us anything about the strength of problem of religious pluralism. Moreover, the fact that the prior odds are low is not particularly significant when there is information highly relevant to G which is being ignored. So again, for the purpose of this discussion, it makes sense to ignore the prior odds and focus on the Bayes’ factor.

End aside.


Therefore, the strength of the problem of religious pluralism is measured by the Bayes’ factor, the ratio of the probability E given G to the probability of E given ~G, or in other words, the degree to which E can be explained by G compared to the degree to which E can be explained by ~G. The smaller this ratio, the stronger the problem.

Let us start by assessing P(E|~G,K). One of the sub-hypotheses under ~G is naturalistic atheism. The atheist would explain the facts of religious diversity as simply the result of false beliefs that have grown up alongside our species and its different cultures. This explanation seems plausible. In fact, under religious pluralism, the explanation is very similar: these different beliefs are just humanity’s various natural attempts to relate to the Ultimate Reality. And there are several world religions where the Ultimate Reality is impersonal or takes no active role in the world, and various religious beliefs grow up naturally just as they do if there is no Ultimate Reality at all.

Which means that, if there is enough background information in K (the existence of human life on earth, for instance) and if E is not construed with too great specificity (so that it can be considered satisfied with any highly diverse set of religious beliefs, not just the particular beliefs that have happened to occur in reality), it is not unreasonable to assume that a significant portion of the probability space under ~G has quite good explanatory power for E. We can thus say that P(E|~G,K) is fairly high; perhaps greater than 0.5, or maybe even close to 1.

This means that the Bayes’ factor will be roughly the same magnitude as P(E|G,K).

So the question now becomes: what is P(E|G,K)? How likely is it, if God exists, that he would create a world full of a great diversity of religions – most of them wrong about who he is and how he wants humankind to relate to him? What reason could God have to do that?

The answer, it seems to me, comes back to the problem of divine hiddenness. In creating the world, God has the choice between revealing himself to everyone, or not revealing himself to everyone (and therefore remaining hidden to some degree). We can suppose that if God were to choose to reveal himself to everyone, that would significantly decrease the degree of religious diversity in the world. (Though even then it may not eliminate it entirely: people could still choose to interpret God’s revelation of himself differently.) If H is the hypothesis that God remains hidden, we can say that P(E|~H,G,K) is close to zero, so that:

P(E|G,K)=P(E|H,G,K) \times P(H|G,K) + P(E|\sim H,G,K) \times P(\sim H|G,K) \simeq P(E|H,G,K) \times P(H|G,K)

Now if God chooses not to reveal himself universally, then to the degree that he remains hidden, the same natural causes for religious diversity can operate as are postulated by atheism and religious pluralism. We can also have religious diversity even in areas where God has revealed himself to some degree, because free creatures can choose to ignore or reject God’s revelation and come up with religion of their own, or they might be deceived by others who have done so. And God may choose to allow the consequences of these free choices (for the kinds of reasons outlined in response to the problem of divine hiddenness and the problem of evil).

All this is to say that we can take the probability P(E|H,G,K) to be fairly high: the hypothesis that God hides is about as good in terms of explanatory power for religious diversity as the hypothesis that God is not there. So P(E|G,K) is roughly the same magnitude as P(H|G,K). And this means that the problem of religious pluralism is derivative: it actually borrows most of its strength from the problem of divine hiddenness.

So speaking in general terms, the reasons that God has for creating a world full of religious diversity are the reasons that he has for choosing to remain hidden – for choosing not to reveal himself universally, but instead only in particular times and places, to particular people. The improbability of religious diversity, given God’s existence, is dependent on the improbability that he would hide.

And, since there are reasons for which God might choose to remain hidden (as I discussed in my earlier post), I don’t think we can say with any confidence that divine hiddenness is very improbable. If it isn’t very improbable, it isn’t sufficient to overcome the (to me, powerful) arguments for God’s existence. Which means that again, the problem of religious pluralism introduces tension into the theistic worldview, but that tension is not insurmountable.

The one caveat I gave in my response to the problem of divine hiddenness becomes very relevant now. The best argument I can think of for saying that P(H|G,K) is very low is this: God cannot have overriding reasons to remain hidden, and allow religious diversity, if it is necessary for humans to accept certain particular religious truths in order to experience the greatest possible good (e.g. salvation or eternal life). If God is all-good, he would not allow humanity to remain in such darkness.

This is the problem of exclusivity, and it is what I will explore in my next post.

The Problem of Evil and Suffering

My last post looked briefly at the problem of divine hiddenness. That problem, to me, is one of the two strongest reasons to disbelieve that God exists. The second of those two reasons is the problem of evil and suffering. It is the question, “If God exists, why is there so much wrong with the world? Why is there so much pain?”

One way to logically formulate the problem goes like this:

  • If God exists, then he is all-good and all-powerful.
  • If God is all-powerful, he creates whichever world he prefers.
  • If God is all-good, then he prefers a world with less evil and suffering than our own.
  • But the evil and suffering of our own world do exist.
  • Therefore, God did not create a world with less evil and suffering than our own.
  • Therefore, God does not exist.

Based on considerations such as the ontological argument, the cosmological argument, and the axiological argument, I accept the first premise. The fourth premise is true by definition. And the intuitive plausibility of the second and third premises is what gives the problem of evil its intellectual force. Pain and suffering are intrinsically less preferable than their absence, making worlds with less of it better in some respect than worlds with more of it. And it certainly seems like God should prefer better worlds, and be able to create them.

“Epicurus’s old questions are still unanswered. Is God willing to prevent evil, but not able? Then he is impotent. Is he able to prevent evil, but not willing? Then he is malevolent. Is he both willing and able? Then whence evil?” – David Hume

Nevertheless, I think there are consideration which should lead us to doubt these crucial two premises of the problem of evil. Contra Hume, many philosophers have answered Epicurus: God is able to prevent evil, and he does not will it to occur – but he can have good reasons to allow it in the world the he creates.

See here and here for two animated videos on the problem of evil and suffering, which cover the topic pretty well in a short format.

The Second Premise

The second premise is that if God is all-powerful, then he can and will create whatever world he wants. There is one important consideration that gives good reason to reject this premise: the possibility of free will.

If God chooses to give genuine free will to his creatures – and there is significant value in him doing so, since, I would argue, it is what makes real loving relationships with and between his creatures possible – then God actually cannot just create whatever world he most wants to exist. In creating human beings with free will, God allows us to be co-actualizers of his reality. He can only create a world in which we make certain free choices if those are the choices that we would freely make.

To put it another way, if God prefers that we choose A, but we instead choose B, then he can only create the reality where we choose A by removing our free will. By allowing us to make free choices, some possibilities are closed off to God. This says nothing to undermine his omnipotence, but it does overturn the intuitive justification for the second premise.

The Third Premise

The more powerful objection to the problem of evil, however, is to reject the third premise on the grounds that God may have morally sufficient reasons for allowing evil and suffering to occur. Free will comes into play here in a significant way as well: it is often put forward that God allows evil because he wants to allow free, morally significant choices to occur, and sometimes such choices result in evil. And he wants free, morally significant choices to occur because they are a necessary condition of loving personal relationships with his creatures, and for his creatures to undergo the moral growth that is necessary for them to experience perfect happiness.

Sometimes philosophers discuss a difference between moral evil and natural evil, the former being the result of free choices by moral agents (such as one person murdering another), and the latter being suffering that does not result from any such choice (such as an animal dying in a forest fire caused by a lightning strike). It is harder to see how natural evil could be justified by the consideration of free will, in addition to moral evil, but in fact I think it can be done.

Natural evil happens because the laws of nature operate in a certain consistent way, and God does not constantly intervene in the natural order that he has created to prevent such evils from occurring. But the fact that he does not constantly intervene actually serves as one of the conditions which makes our free will significant. The existence of consistent natural world enables us to reasonably predict what the consequences of our free choices will be, and provides us with opportunities to choose good over evil that we would not otherwise have.

Moreover, I would argue there is a kind of beauty in the natural world that would be diminished if it were constantly disrupted by God to prevent every kind of pain and suffering. We also have to consider that not all pain and suffering is completely bad: it is an intrinsic part of diverse ecosystems, it can serve to prevent further harm, and it can actually draw people closer to God. From a Christian perspective, there are verses in the Bible indicating God’s approval of the natural world, complete with instances of apparent evil (such as predation).

So those are some reasons why God might permit evil to occur. Here is another article giving another set of goods which may require allowing evil in order to be realized. I think these are worth mentioning:

  • As I have already said, a knowable natural world providing an arena for morally significant free choices is a great good. And there is aesthetic value in the order of the natural world itself.
  • Being able to form our own character in response to evil and suffering is good. Such character growth, in fact, may be the only way for finite created beings to fully enter into a relationship with God and experience perfect happiness.
  • The existence of evil and suffering allows God’s redemptive response to that evil and suffering, which is very good. More generally, I think true stories of conquering evil are morally valuable.
  • There are relational goods that may only be realized in response to evil (for example, sacrificing oneself for another, or love relationships forged by experiencing suffering together).

All of this goes to show that God may have reasons to allow some evil and suffering, but does it show that he has reasons to allow as much evil and suffering as exists in the actual world? The answer to that is, for all we know, it certainly could. The fact is that there is a lot of evil in the world that seems to serve no purpose – but from our limited perspective, we cannot expect to be able to see all of the reasons that God has for any specific instance of evil. The huge complexity of the world means that we can only see so far – whereas God’s foreknowledge stretches from the beginning to the end of time.

The other thing to consider when trying to evaluate whether the amount of evil in the world can be justified is that, if Christianity is true, there is the potential of an eternity of perfect happiness to counterbalance any extent of suffering experienced in our mortal lives, no matter how great. And, I think, the issue of free will that I have been talking about plays into that.

In order for a community of finite, created beings to experience perfect happiness in relationship with God and with each other, for eternity, they have to make certain choices. They have to choose not to pursue their own happiness at the expense of others. They have to make wise choices that will not lead to harm. Because God is perfectly good and only he knows completely what is best, they have to choose to submit to God and allow him to guide them. And they will have to go on making these choices forever.

Though some Christians believe free will is going to be taken away or changed somehow when we are brought into the new creation, so that it is no longer possible for us to sin, I think that may not be the case: I am inclined to think that free will is necessary for a true loving relationship, whether we are in heaven or not. But that raises an interesting question, to me.

What if all our experiences of evil and suffering – our individual experiences, including our moral growth, and the collective experience of humanity and all of the lessons learned from “doing things our own way” – is exactly what God foreknows is needed to create a community of moral agents who can experience perfect happiness together forever? What if, by allowing a finite amount of evil and suffering, God secures an infinite amount of good, freely chosen by his creatures?

And what if, because of God’s love for us, every individual human life has unique, irreplaceable value to him? What if the amount of evil and suffering in our world is precisely what God must allow, and no more, in order for all the goods of this world to be realized – including eternal life for each of the specific individuals who freely choose to follow him? If these last two “what if’s” are possible, then there could actually be a respect in which this world is better than any other possible reality, which would be enough to justify God’s decision to create it.


Often, the problem of evil is raised up as the problem for belief in God. But in the end I do not think it is anywhere near a definitive disproof of God’s existence. There could very well be reasons for God to allow evil. We can think of a number of such reasons in general. And given our limited ability to survey the vast complexity and scope of history, we should not expect to be able to see God’s reasons for allowing specific evils in many cases.

So again, the problem of evil presents a tension in the theistic worldview, but not one that cannot be overcome. Perhaps the biggest challenge of the problem of evil (especially when combined with the problem of divine hiddenness) is the emotional one: pain hurts, and it is natural to ask why God lets painful things happen to us or to loved ones, or why he does not at least show up personally to comfort us when those things happen.

All the philosophizing in the world is probably not enough to answer someone going through a time that makes them ask those questions, but I do appreciate what William Lane Craig has to say on that subject: although the problem of evil introduces a tension in the Christian story, in the end, it is the Christian story that provides the greatest comfort in the face of evil. He says it better than I do, so rather than elaborate further, I will just link it here. I encourage you to give it a look.